Monotone metric tensors in Quantum Information Geometry

• URL: http://arxiv.org/abs/2203.10857v2
• Date: Tue, 12 Sep 2023 09:50:59 GMT
• Title: Monotone metric tensors in Quantum Information Geometry
• Authors: Florio M. Ciaglia, Fabio Di Cosmo, Fabio Di Nocera, Patrizia Vitale
• Abstract summary: We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is naturally suited to investigate the comparison with the classical case of probability distributions.

Related papers

• Quantum geometry of the parameter space: a proposal for curved systems [0.0]
  We introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the quantum geometric tensor. The parameter-dependent metric modifies the behavior of both the quantum metric tensor and Berry curvature in a purely geometric way.
  arXiv  Detail & Related papers  (2024-03-14T18:51:26Z)
• Generalized quantum geometric tensor for excited states using the path integral approach [0.0]
  The quantum geometric tensor encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states. We then generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates.
  arXiv  Detail & Related papers  (2023-05-19T08:50:46Z)
• Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography [2.0758589947805572]
  In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT) We propose and experimentally implement a complete Bloch state tomography to measure eigenfunction of an optical Raman lattice for ultracold atoms.
  arXiv  Detail & Related papers  (2023-01-15T13:05:01Z)
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers [0.0]
  We establish relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. We show that topological indices are bounded by the quantum volume determined by the quantum metric. This work suggests unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.
  arXiv  Detail & Related papers  (2021-06-01T21:10:48Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs [62.997667081978825]
  We study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph.
  arXiv  Detail & Related papers  (2020-03-25T02:46:14Z)
• Finite Deformations of Quantum Mechanics [0.0]
  We investigate modifications of quantum mechanics that replace the unitary group in a finite dimensional Hilbert space with a finite group. We show that Kornyak's proposal to understand QM as classical dynamics on a Hilbert space of one dimension higher than that describing the universe can probably be a model of the world we observe.
  arXiv  Detail & Related papers  (2020-01-21T17:35:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.